The invention relates to a masonry system having masonry elements of various sizes and formats upon which masonry element can be laid. Structural units for such a masonry system, in particular for dry masonry walls, are known from European patent EP 0 490 168 B 1. The structural units comprise elements similar to hollow blocks having a frame-like elevation on the surface so that a joint is produced when structural units are laid thereover. The structural units have through openings into which concrete, reinforced with steel bars as appropriate, can be poured in order to achieve greater strength of the masonry system. Such structural units have one or two faces, which correspond to the concrete texture or must be treated in order to create a special texture. A colored building blocks can be produced; however, the costs therefore are relatively high because the building blocks must be manufactured with the decorative mix throughout. From German patent DE 20 2005 017 511 U1 it is further known to use structural units corresponding to the previously cited European patent and to clad the face of such units with at least one surface piece so that a texture becomes visible. Here again the building blocks are massive and heavy and retain the concrete texture apart from the surface piece.